A theoretical model of nanowire formation by the vapor-liquid-solid mechanism during molecular beam epitaxy and related growth techniques is presented. The model unifies the conventional adsorption-induced model, the diffusion-induced model, and the model of nucleation-mediated growth on the liquid-solid interface. The concentration of deposit atoms in the liquid alloy, the nanowire diameter, and all other characteristics of the growth process are treated dynamically as functions of the growth time. The model provides theoretical length-diameter dependences of nanowires and the dependence of the nanowire length on the technologically controlled growth conditions, such as the surface temperature and the deposition thickness. In particular, it is shown that the length-diameter curves of nanowires might convert from decreasing to increasing at a certain critical diameter and that the nanowires taper when their length becomes comparable with the adatom diffusion length on the sidewalls. The theoretical dependence of the nanowire morphology on its lateral size and length and on the surface temperature are compared to the available experimental data obtained recently for Si and $\mathrm{GaAs}$ nanowires.

• Received 11 October 2005

DOI:https://doi.org/10.1103/PhysRevE.73.021603